Provided by: liblapack-doc_3.3.1-1_all bug


       LAPACK-3 - reduces the M-by-N ( M<=N ) real upper trapezoidal matrix A to upper triangular
       form by means of orthogonal transformations



           INTEGER        INFO, LDA, LWORK, M, N

           DOUBLE         PRECISION A( LDA, * ), TAU( * ), WORK( * )


       DTZRZF reduces the M-by-N ( M<=N ) real upper trapezoidal matrix  A  to  upper  triangular
       form by means of orthogonal transformations.
        The upper trapezoidal matrix A is factored as
           A = ( R  0 ) * Z,
        where Z is an N-by-N orthogonal matrix and R is an M-by-M upper
        triangular matrix.


        M       (input) INTEGER
                The number of rows of the matrix A.  M >= 0.

        N       (input) INTEGER
                The number of columns of the matrix A.  N >= M.

        A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
                On entry, the leading M-by-N upper trapezoidal part of the
                array A must contain the matrix to be factorized.
                On exit, the leading M-by-M upper triangular part of A
                contains the upper triangular matrix R, and elements M+1 to
                N of the first M rows of A, with the array TAU, represent the
                orthogonal matrix Z as a product of M elementary reflectors.

        LDA     (input) INTEGER
                The leading dimension of the array A.  LDA >= max(1,M).

        TAU     (output) DOUBLE PRECISION array, dimension (M)
                The scalar factors of the elementary reflectors.

        WORK    (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK))
                On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

        LWORK   (input) INTEGER
                The dimension of the array WORK.  LWORK >= max(1,M).
                For optimum performance LWORK >= M*NB, where NB is
                the optimal blocksize.
                If LWORK = -1, then a workspace query is assumed; the routine
                only calculates the optimal size of the WORK array, returns
                this value as the first entry of the WORK array, and no error
                message related to LWORK is issued by XERBLA.

        INFO    (output) INTEGER
                = 0:  successful exit
                < 0:  if INFO = -i, the i-th argument had an illegal value


        Based on contributions by
          A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
        The factorization is obtained by Householder's method.  The kth
        transformation matrix, Z( k ), which is used to introduce zeros into
        the ( m - k + 1 )th row of A, is given in the form
           Z( k ) = ( I     0   ),
                    ( 0  T( k ) )
           T( k ) = I - tau*u( k )*u( k )**T,   u( k ) = (   1    ),
                                                       (   0    )
                                                       ( z( k ) )
        tau is a scalar and z( k ) is an ( n - m ) element vector.
        tau and z( k ) are chosen to annihilate the elements of the kth row
        of X.
        The scalar tau is returned in the kth element of TAU and the vector
        u( k ) in the kth row of A, such that the elements of z( k ) are
        in  a( k, m + 1 ), ..., a( k, n ). The elements of R are returned in
        the upper triangular part of A.
        Z is given by
           Z =  Z( 1 ) * Z( 2 ) * ... * Z( m ).

 LAPACK routine (version 3.3.1)             April 2011                            DTZRZF(3lapack)